Field of Invention
The present invention relates broadly to protecting the privacy of information and devices. The processes and device are generally used to maintain the privacy of information transmitted through communication and transmission systems. For example, the hiding processes may be used to conceal one or more public keys transmitted during a Diffie-Hellman exchange; in some embodiments, the public keys may be transmitted inside noise via IP (internet protocol). These processes and devices also may be used to hide passive public keys stored on a computer or another physical device such as a tape drive. In some embodiments, symmetric cryptographic methods and machines are also used to supplement the hiding process.
Typically, the information—public key(s)—is hidden by a sending agent, called Alice. Alice transmits one or more hidden public key(s) to a receiving agent, called Bob. The receiving agent, Bob, applies an extraction process or device. The output of this extraction process or device is the same public keys that Alice computed before hiding and sending them. Eve is the name of the agent who is attempting to obtain or capture the public keys transmitted between Alice and Bob. One of Alice and Bob's primary goals is to assure that Eve cannot capture the public keys that were hidden and transmitted between Alice and Bob. The hiding of public keys can help stop Eve from performing a man-in-the-middle attack on Alice and Bob's public key exchange because in order to successfully launch a man-in-the-middle attack, Eve must know Alice and Bob's public keys.
Prior Art
The subject matter discussed in this background section should not be assumed to be prior art merely as a result of its mention in the background section. Similarly, a problem mentioned in the background section or associated with the subject matter of the background section should not be assumed to have been previously recognized in the prior art. The subject matter in the Summary and some Advantages of Invention section represents different approaches, which in and of themselves may also be inventions, and various problems, which may have been first recognized by the inventor.
In information security, a fundamental problem is for a sender, Alice, to securely transmit a message M to a receiver, Bob, so that the adversary, Eve, receives no information about the message. In Shannon's seminal paper [1], his model assumes that Eve has complete access to a public, noiseless channel: Eve sees an identical copy of ciphertext C that Bob receives, where C(M, K) is a function of message M lying in message space  and secret key K lying in key space .
In this specification, the symbol P will express a probability. The expression P(E) is the probability that event E occurs and it satisfies 0≤P(E)≤1. For example, suppose the sample space is the 6 faces of die and E is the event of rolling a 1 or 5 with that die and each of the 6 faces is equally likely. Then P(E)= 2/6=⅓. The conditional probability
      P    ⁡          (              A        ❘        B            )        =                    P        ⁡                  (                      A            ⋂            B                    )                            P        ⁡                  (          B          )                      .  P(A∩B) is the probability that event A occurs and also event B occurs. The conditional probability P(A|B) expresses the probability that event A will occur, under the condition that someone knows event B already occurred. The expression that follows the symbol “|” represents the conditional event. Events A and B are independent if P(A∩B)=P(A)P(B).
Expressed in terms of conditional probabilities, Shannon [1] defined a cryptographic method to be perfectly secret if P(M)=P(M|Eve sees ciphertext C) for every cipher text C and for every message M in the message space . In other words, Eve has no more information about what the message M is after Eve sees ciphertext C pass through the public channel. Shannon showed for a noiseless, public channel that the entropy of the keyspace  must be at least as large as the message space  in order to achieve perfect secrecy.
Shannon's communication secrecy model [1] assumes that message sizes in the message space are finite and the same size. Shannon's model assumes that the transformations (encryption methods) on the message space are invertible and map a message of one size to the same size. Shannon's model assumes that the transformation applied to the message is based on the key. In the prior art, there is no use of random noise that is independent of the message or the key. In the prior art, there is no notion of being able to send a hidden or encrypted message inside the random noise where Eve is not necessarily revealed the size of the message. In the prior art, there is no notion of using random noise to hide the secret channel and transmitting a key inside this channel that is indistinguishable from the noise.
Quantum cryptography was introduced by Weisner and eventually published by Bennett, Brassard, et al. [2, 3]. Quantum cryptography based on the uncertainty principle of quantum physics: by measuring one component of the polarization of a photon, Eve irreversibly loses her ability to measure the orthogonal component of the polarization. Unfortunately, this type of cryptography requires an expensive physical infrastructure that is challenging to implement over long distances [4, 5]. The integrity of the polarization depends upon this physical infrastructure; it is possible for Eve to tamper with the infrastructure so that Alice and Bob, who are at the endpoints, are unable to adequately inspect or find this tampering. Furthermore, Alice and Bob still need a shared, authentication secret to successfully perform this quantum cryptography in order to assure that Eve cannot corrupt messages about the polarization bases, communicated on Alice and Bob's public channel.